It is one of the most striking sights of autumn. As days shorten and the weather cools, black clouds gather over Britain's skies. These dark spectacles have nothing to do with the weather, however. They are made up of thousands of starlings swirling and swooping in the air, performing aerial ballets that appear to be synchronised. Sometimes, flocks shift in shape from globes to hourglasses, thickening and thinning in the atmosphere.

The behaviour of these murmurations of starlings has puzzled scientists for years. Some researchers have argued that they are created by one or two starlings who lead the rest of the birds in these strange performances. Others have suggested more intriguing causes, such as the British ornithologist Edmund Selous who claimed the birds were responding to telepathic signals from their mates. But now a Dutch scientist, Charlotte Hemelrijk, of Groningen University, in an article in the online journal PLoS ONE, has proposed a far simpler idea: that this seemingly sophisticated behaviour can be explained using only a few simple behavioural rules. And not only are these rules true for starlings, she says, they are also true for other creatures such as fish.

In the case of starlings, Hemelrijk and her colleagues simply assumed that the birds are attracted to each other; that they move in the same direction as they return home to roosts after feeding; that they try to avoid colliding with each other; that they fly at the same speeds and that they bank when turning in the sky.

The scientists then created computer simulations of starlings that behaved by these rules and found that these shifts in the shape of flocks that have been observed in starlings could be shown to arise from relatively simple manoeuvres. For example, a flock that is flat and wide almost instantly becomes long and narrow merely by executing a basic 90-degree turn – perhaps as the result of an approach by a predator – because birds that were once flying abreast were now flying behind each other. In other words, these ballets in the sky are the automatic expression of simple acts of self-organisation.

Other factors, such as wind speed, were not included in the team's calculations, Hemelrijk admits, and will have to be addressed in future studies. Nevertheless, she insists, their model provides a valuable platform for understanding complex behaviour according to simple rules.